Question

Rosie's Florist borrows $300,000 to be paid off in six years. The loan payments are semiannual with the first payment due in six months, and interest is at 6%. What is the amount of each payment

Answer 1

To calculate each semiannual payment for Rosie's Florist's $300,000 loan at a 6% annual interest rate with payments over six years, the formula for an ordinary annuity is used. After substituting the values into the formula, one can solve for the payment amount.

Step-by-step explanation:

Calculating the Semiannual Loan Payment

To find out the amount of each semiannual payment for Rosie's Florist, we need to use the formula for an ordinary annuity because the payments are regular and the interest rate is applied semiannually. The formula to find the payment R for an ordinary annuity is:

PV = R × [(1-(1 + i)^-n) / i]

Where:

• PV is the present value or amount of the loan, which is $300,000
• i is the interest rate per period, which is 0.06/2 = 0.03 (6% per annum with semiannual payments)
• n is the total number of payments, which is 6 years × 2 times a year = 12

By substituting the given values into this formula, the payment R can be calculated. The actual computation involves solving for R through algebraic manipulation or using a financial calculator or spreadsheet software to perform the calculations.

After computing, we will find that each semiannual payment ensures that Rosie's Florist pays back the $300,000 loan over 12 semiannual periods with a 6% annual interest rate compounded semiannually.

Answer 2

$34000

Step-by-step explanation:

This can be calculated as follows. Assuming Interest rate is annual.

Principal amount + Interest amount = Total payable amount per payment

Principal amount = $300,000/6 years = $50,000 annually or $25000 semi-annually

Interest amount = $300,000 * 0.06 = $18000 annually or $9000 semi-annually

Total Payable = $25,000 + $9000 = $34,000 per payment semi-annually.

Hope that helps.